Iceblossom

I think Bear is right, this is probably easier to do by hand, but it can be done by sewing and I'll do a bit of research.

Before I research, if you asked me to make one based on the picture -- I like the solid thin petal things in the center, but I would probably divide the center into wedges right down the middle of the thin petals. There are 6 sections, so 60 degree triangles basically. Then I'd either work on out to the edges, or I would do it in rings. Although I often disparage specialty rulers, there is such a thing as having the right tool for the job and if I did it in rings, I would want the correct size template rings, or I do have a couple different circle cutting things.

Edit: The gentle curves should be reasonably easy to piece by machine but may take a bit of getting used to.

Edit 2: One of the other make it easier techniques would be to simply hand applique the thin slivers on top of the center circle.